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Beliebt Rechnen >

integral from 1 to 16 of x^{1/2}ln(x)

Lösung

\int_{1}^{16} x^{\frac{1}{2}} ln (x) d x

Lösung

- 28 + \frac{512}{3} ln (2)

+1

Dezimale

90.29711 \dots

Schritte zur Lösung

\int_{1}^{16} x^{\frac{1}{2}} ln (x) d x

Wende die partielle Integration an

= [\frac{2}{3} x^{\frac{3}{2}} ln (x) - \int \frac{2}{3} x^{\frac{1}{2}} d x]_{1}^{16}

\int \frac{2}{3} x^{\frac{1}{2}} d x = \frac{4}{9} x^{\frac{3}{2}}

= [\frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}}]_{1}^{16}

Berechne die Grenzen:

- 28 + \frac{512}{3} ln (2)

= - 28 + \frac{512}{3} ln (2)

Graph

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